Analysis of the Influence Structure Between Design Factors and Heat Source Equipment Capacity: A Case Study on Office Building Design with a Central Heat Source System in Warm Regions of Japan

Abstract

To achieve carbon neutrality by 2050, the realization of Net-Zero-Energy Buildings (ZEBs) and the proper design of heat source equipment capacity are essential. Consequently, numerous studies have been conducted to prevent overdesign. However, most previous studies have analyzed the factors influencing heat source equipment capacity as independent and isolated variables. In actual design practice, however, factors interact in complex and interdependent ways, yet few studies have considered the interrelationships among these factors or conducted a structural and comprehensive analysis of their influence on heat source equipment capacity. Therefore, this study aims to quantitatively model the influence structure between design factors and heat source equipment capacity using Structural Equation Modeling (SEM), focusing on office buildings with a central heat source system in warm regions of Japan. This research offers a novel perspective not found in previous studies by structurally and comprehensively analyzing the relationship between design factors and heat source equipment capacity, examining the interactions between the factors and their impact on equipment capacity in stages. As a result, by modeling the influence structure, it was confirmed that the diversity factor, handling of internal heat gain, and appropriate design based on actual building usage, such as internal heat gain and the safety factor, are effective for optimizing heat source equipment capacity. Moreover, the result also confirmed that industry, company size, building scale, building use, and software influence the above design factors. This study is a case study that focuses on the maximum heat load calculation in mechanical equipment design and attempts to model the influence of design factors and heat source equipment capacity. However, it is expected that future studies using the same methodology as this study and incorporating additional factors not discussed in this study, and expanding across various regions, will provide a valuable and effective approach to optimizing heat source equipment capacity.

1. Introduction

The building and construction sector accounts for approximately 21% of global greenhouse gas emissions. In 2022, buildings were responsible for 34% of the world’s energy demand and 37% of energy-related and process-related CO₂ emissions [1,2]. Therefore, minimizing the energy consumption of buildings is essential for achieving global carbon reduction goals. In response, various countries are implementing policies to promote building decarbonization. In the European Union (EU), the Energy Performance of Buildings Directive (EPBD) has been revised to achieve a fully decarbonized building stock by 2050 [3], coming into effect across all EU member states in May 2024. Given that 85% of EU buildings were constructed before 2000—75% of which still have low energy performance—the EPBD aims to introduce minimum energy standards for non-residential buildings and encourage renovations of the least energy-efficient buildings. Similarly, California, USA, was the first state to implement its own green building standards, CALGreen, which is updated every three years [4]. Additionally, in July 2024, the Non-Residential CALGreen New Mandatory Embodied Carbon Reduction Regulations were introduced to reduce embodied carbon in non-residential buildings. Japan has also set a target to ensure that newly constructed houses and buildings achieve Net Zero Energy House (ZEH) and Net Zero Energy Building (ZEB) standards starting in 2030 [5]. As part of stricter energy regulations, from April 2024, Japan has strengthened energy efficiency standards for large-scale non-residential buildings by approximately 20%, with similar measures planned for medium-scale non-residential buildings from 2026. Moreover, various building sustainability assessment systems such as Building Research Establishment Environmental Assessment Methodology (BREEAM), Leadership in Energy and Environmental Design (LEED), and Comprehensive Assessment System for Built Environment Efficiency (CASBEE) have been widely adopted worldwide [6].

Among all building types, office buildings consume the largest share of total building energy consumption (approximately 23%), making ZEB implementation for office buildings essential for decarbonization efforts. Japan’s Ministry of Land, Infrastructure, Transport, and Tourism emphasizes that optimizing heat source equipment capacity and improving HVAC efficiency are crucial for achieving ZEB in office buildings [7]. Studies by Djunaedy et al. [8] and Kim et al. [9] have long emphasized the importance of appropriate system design during new construction and renovation to ensure energy efficiency. However, in practice, oversized heat source designs are often implemented as a precaution against extreme weather conditions and uncertainty in demand predictions, leading to inefficiencies due to partial load operation [10]. To address this issue, numerous studies have explored system design optimization and HVAC system efficiency [11,12,13]. Research has demonstrated that modifications to dampers [14], filters [15], humidifiers/dehumidifiers [16], heating and cooling coils [17], ducts, and fans [18] can significantly reduce energy consumption and improve system performance.

Focusing specifically on heat source equipment capacity design, numerous studies have investigated internal heat gain surveys and energy simulations as methods to avoid overdesign [19,20,21]. For example, Kim et al. [22] analyzed long-term changes in internal heat gains in office buildings, demonstrating how these loads evolve over time and influence energy consumption and HVAC system design. Additionally, Carlander et al. [23] conducted energy simulations for office buildings in three different regions of Sweden, examining the effects of building location, orientation, facade design, and internal heat gains on energy demand. Their findings highlight that increased internal heat gain significantly impacts total energy demand. Research has also explored safety factors in design. Urayama et al. [24] estimated that considering all safety factors increases maximum heat load by 21%. Furthermore, several studies have examined design methods to prevent overdesign. Lapinskienė et al. [25] and Jenkins et al. [26] used simulations to show that managing internal heat gains is an effective strategy for reducing cooling and heating loads. Kikuta et al. [27] investigated diversity factors and proposed a quantitative method for determining these factors based on occupant behavior.

As discussed above, numerous studies have been conducted from various perspectives to prevent overdesign. However, previous research has generally treated each factor such as the internal heat gain, safety factor, and diversity factor as an independent and isolated variable, analyzing the relationship between each factor and heat source equipment capacity separately. However, in actual design practice, it is thought that there are interrelationships between these factors, such as estimating the internal heat gain or safety factor a little larger and considering the diversity factor. But these interrelationships have not been adequately addressed in previous studies. Furthermore, Yılmaz et al. [28] and Asim et al. [29] found that design policies differ based on company size and industry. Similarly, Papadakis et al. [30] and Munguia et al. [31] indicated that internal heat gain varies depending on building use (private or public). However, previous research has not comprehensively analyzed the interrelationships between factors such as industry, company size, and building use, nor how these differences in building use influence internal heat gain.

Thus, in actual design practice, design is inherently considered not to be a one-way relationship for each factor, but a complex relationship in which various factors other than those mentioned above mutually influence each other. However, in previous studies, it has not been sufficiently clarified what kind of interrelationships these factors have and how they relate to heat source equipment capacity. There is a lack of research on how each design factor interacts with the capacity of heat source equipment in a step-by-step manner, and how this relationship to the capacity of heat source equipment is structurally and comprehensively organized and quantitatively evaluated.

Considering these research gaps, this study aims to clarify the influence structure between design factors and heat source equipment capacity in a stepwise manner and to clarify the influence structure of each design factor and heat source equipment capacity. The structural and comprehensive analysis of the relationship between design factors and heat source equipment capacity, and the step-by-step analysis of the interrelationship between each design factor and heat source equipment capacity, is a new perspective of this study not found in previous studies. This study focuses on maximum heat load calculation in mechanical equipment design, categorizing design factors into the following groups: personal attributes (years of experience, industry, and company size), design conditions (building use, building scale, and software), calculation conditions (internal heat gain, ventilation rates per person, and safety factors) and design methods (handling of internal heat gain and diversity factor). However, it is expected that future studies using the same methodology as this study and incorporating additional factors not discussed in this study, and expanding across various regions, will provide a valuable and effective approach to optimizing heat source equipment capacity.

2. Research Flow

The research flow of this study is shown in Figure 1. First, a questionnaire survey was conducted. Following this, analytical questions and target respondents were extracted. As a preliminary analysis for modeling the influence structure, a statistical analysis was performed to examine the factors by which each design factor affects heat source equipment capacity. Subsequently, based on the findings obtained from the statistical analysis and previous studies, a research hypothesis model was developed. The model was then constructed using Structural Equation Modeling (SEM). Structural Equation Modeling is a multivariate statistical modeling method that allows for the representation of multiple causal relationships, measuring interactions and the strength of influence between variables. In recent years, studies utilizing Structural Equation Modeling have been conducted in various research fields [32,33], and it has been validated as a method that can analyze the interrelationships of each factor step by step and analyze the overall impact structure in a structured and comprehensive manner, which is why it was also employed in this study.

The details of the questionnaire and the process of extracting analytical questions and target respondents are presented in Section 3, while the results of the statistical analysis and modeling are discussed in Section 4.

3. Material and Methods

3.1. Questionnaires

This study surveyed current practices in designing heat sources and HVAC systems for office buildings. Three organizations—the Japanese Association of Building Mechanical and Electrical Engineers (JABMEE), the Japan Federation of Mechanical and Electrical Consulting Firms Association (JAFMEC), and the Institute for Built Environment and Carbon Neutral for SDGs (IBECs)—cooperated to carry out the survey. Mechanical equipment designers affiliated with these organizations with experience in office building design were invited to respond. Respondents provided answers based on personal experience rather than company policy or perspectives. The survey was developed to address Japan’s Building Equipment Design Standards [34] and consisted of four sections (a total of 22 questions): “Respondent Attributes”, “Maximum Heat Load Calculation for Heat Source Equipment Capacity Design”, “Design Methods for Heat Source and HVAC Systems”, and “ZEB Design”.

The section on respondent attributes included questions about industry, company size (number of employees engaged in mechanical equipment design), the energy-conservation regional classification most frequently used in their design projects [35], the ratio of private to public projects, experience with central or individual heat sources, and the scale of buildings they have designed.

The section on maximum heat load calculations for heat source equipment capacity included questions about the design standards, calculation software, reference methods, indoor conditions, internal heat gain, ventilation rate per person, handling of internal heat gain in heating load calculations, and safety factors. The Building Equipment Design Standards [34] specify internal heat gain values as follows: person density of 0.1–0.2 persons/m², lighting heat of 9–11 W/m² for LED lighting, 16–25 W/m² for fluorescent lighting, and equipment heat of 15–30 W/m². In addition, the importance of ventilation has been reemphasized due to the impact of the COVID-19, with 30 CMH/person recommended as the standard ventilation rate in Japan.

Table 1. Safety factors in Japan.

Safety Factors		Set Value
		Cooling	Heating
Intermittent Operation Coefficient	A factor that accounts for the additional load required during the start-up period of cooling or heating when equipment is operated intermittently	1.1	1.0~1.1
Safety Factor	A factor to provide a margin for unforeseen loads or deviations from the intended operational conditions	1.0~1.1	1.0~1.1
Fan Load Coefficient	A factor that considers additional load due to airflow resistance and other loads impacting the fan	1.05	―
Pump Load× Piping Loss× Equipment Load Coefficient	A factor that considers pressure loss and friction loss within pumps, piping, and equipment	1.00~1.05	―
Piping Loss Coefficient	A factor that accounts for friction loss and thermal loss within the piping	―	1.00~1.05
Equipment Load Coefficient	A factor that provides a buffer for operation exceeding the rated capacity of the equipment	―	1.00~1.05
Aging Coefficient	A factor that considers reduced efficiency due to equipment degradation over time	1.05	1.05
Capacity Compensation Coefficient	A factor that compensates for differences between design conditions and actual operating conditions	1.05	1.05

presents the safety factors stipulated in the Building Equipment Design Standards.

In the section on design methods for heat source and HVAC systems, questions covered safety factors, approaches to partial load operation, the diversity factor, and heat source equipment capacity. The term “heat source equipment capacity” here refers to the capacity based on the maximum heat load before equipment selection, not the actual capacity of the installed equipment. All heat source equipment capacities referenced in this study are based on the maximum heat load before equipment selection.

The ZEB section included design questions related to the BPI (Building Plaster Index), internal heat gain, and heat source equipment capacity.

The survey was conducted twice, from December 2022 to January 2023 and again in July 2023, and it resulted in 202 valid responses.

3.2. Extraction of Analytical Question and Target Subjection, and Statistical Analysis

This study focused on the design of central heat source systems. Therefore, in the statistical analysis, only respondents who indicated they had experience designing central heat sources were included. To eliminate regional differences in heat source equipment capacity, the analysis was further narrowed to respondents from the “Region 6” energy-conservation classification [35], which had the highest number of responses and is the region with the most design experience (cooling: n= 106, heating: n= 104). Region 6, which includes Tokyo, Osaka, and Aichi, the metropolis of Japan, is a relatively warm area within the country and predominantly requires cooling in office buildings.

The analysis focused on questions that significantly impact the final heat source equipment capacity (

Table 2. Questionnaire items.

Major Category	Sub-Category	Question Item		Options
		Cooling	Heating
Personal Attributes	Years of Experience	Years of practical experience in mechanical equipment design		Direct numerical input
	Industry	Current industry of employment		General Contractor
				Architectural Firm
				Mechanical and Electrical Contractor
				Mechanical and Electrical Design Firm
				Others
	Company Size	Number of employees engaged in mechanical equipment design		Less than 10
				10–50
				50–100
				More than 100
				Unknown
Design Conditions	Building Use	Ratio of private (tenant) to public		Private 100% Public 0%
				Private 75% Public 25%
				Private 50% Public 50%
				Private 25% Public 75%
				Private 0% Public 100%
	Building Scale	Common building scale in design experience		Less than 2000 m2
				2000–10,000 m2
				More than 10,000 m2
	Software	Current software or calculation method [34,36,37,38,39,40,41]		Building Equipment Design Standards
				Design Maximum Heat Load Calculation Method
				Simplified Heating and Colling Load Calculation Method
				MICRO-PEAK2000 ver
				MICRO-PEAK2010 ver
				NewHASP
				BEST
				HASPEE
				Referencing similar properties
Calculation Conditions	Internal Heat Gain	Person Density (people/m2)		Direct numerical input
		Lighting Heat (W/m2)
		Equipment Heat (W/m2)
	Ventilation Rate Per Person	Ventilation Rate Per Person (CMH/person)		Direct numerical input
	Safety Factors	Intermittent Operation Coefficient	Aging Coefficient	Use less than set value
		Fan Load Coefficient		Use set value
		Aging Coefficient	Capacity Compensation Coefficient	Use greater than set value
		Capacity Compensation Coefficient
				Unknown
		Safety Factor	Safety Factor	Use less than minimum value
			Intermittent Operation Coefficient
				Use minimum value
				Use Median value
		Pump Load× Piping Loss× Equipment Load Coefficient	Piping Loss Coefficient	Use maximum value
				Use greater than maximum value
			Equipment Load Coefficient
				Unknown
Design Methods	Handling of Internal Heat Gain	―	Handling of Internal Heat Gain [25,26]	Should be considered
				Should not be considered
	Diversity Factor	Practical handling of Diversity Factor [27]		Considered in design
				Not considered but feels necessary
				Not considered
Heat Source Equipment Capacity		Heat source equipment capacity per air-conditioning area (W/m2)		Direct numerical input

). Since it is necessary to convert the answers into numerical values for statistical analysis, we converted the choices as shown in

Table 3. Converted options.

Question Item		Options	Converted Options
Cooling	Heating
Years of practical experience in mechanical equipment design		Direct numerical input	Direct numerical input
Current industry of employment		General Contractor	0. General Contractor
		Architectural Design Office	1. Architectural Firm
		Mechanical and Electrical Contractor	2. Mechanical and Electrical Contractor
		Mechanical and Electrical Design Firm	3. Mechanical and Electrical Design Firm
		Others
Number of employees engaged in mechanical equipment design		Less than 10	0. Less than 10
		10–50	1. 10–50
		50–100	2. 50–100
		More than 100	3. More than 100
		Unknown
Ratio of private (tenant) to public		Private 100% Public 0%	0. Private
		Private 75% Public 25%	1. Public
		Private 50% Public 50%	* More than 50% private designed with private *
		Private 25% Public 75%
		Private 0% Public 100%
Common building scale in design experience		Less than 2000 m2	0. Less than 10,000 m2
		2000–10,000 m2	1. More than 10,000 m2
		More than 10,000 m2
Current software or calculation method		Building Equipment Design Standards	0. Only Building Equipment Design Standards
		Design Maximum Heat Load Calculation Method
			1. Combined Use of Building Equipment Design Standards
		Simplified Heating and Colling Load Calculation Method
			2. Non-use of Building Equipment Design Standards
		MICRO-PEAK2000 ver
		MICRO-PEAK2010 ver
		NewHASP
		BEST
		HASPEE
		Referencing similar properties
Person Density Lighting Heat Equipment Heat	―	Direct numerical input	Person Density (people/m2):
			0. Use less than 0.1
			1. Use 0.1~0.15
			2. Use 0.15
			3. Use 0.15~0.3
			4. Use greater than 0.3
			Lighting Heat (W/m2):
			0. Use less than 9.0
			1. Use 9.0~10
			2. Use 10
			3. Use 10~11
			4. Use greater than 11
			Equipment Heat (W/m2):
			0. Use less than 15
			1. Use 15~22.5
			2. Use 22.5
			3. Use 22.5~30
			4. Use greater than 30
Ventilation Rate Per Person (CMH/person)		Direct numerical input	Direct numerical input
Intermittent Operation Coefficient	Aging Coefficient	Use less than set value	0. Use less than set value~
	Capacity Compensation Coefficient	Use set value
Fan Load Coefficient		Use greater than set value	2. Use greater than set value
Aging Coefficient		Unknown
Capacity Compensation Coefficient
Safety Factor	Safety Factor	Use less than minimum value	0. Use less than minimum value ~
Pump Load× Piping Loss× Equipment Load Coefficient	Intermittent Operation Coefficient
		Use minimum value	4. Use greater than maximum value
	Piping Loss Coefficient	Use Median value
		Use maximum value
	Equipment Load Coefficient	Use greater than maximum value
		Unknown
―	Handling of Internal Heat Gain	Should be considered	0. Should be considered
		Should not be considered	1. Should not be considered
Practical handling of Diversity Factor		considered in design	0. Considered in design
		Not considered but feels necessary	1. Not considered
		Not considered
Heat Source Equipment Capacity (W/m2)		Direct numerical input	Direct numerical input

and conducted the analysis. Years of experience, ventilation rate per person, and heat source equipment capacity were used as they are, while industry, company size, building use, building scale, software, handling of internal heat gain, and the diversity factor were partially merged into dummy variables and used in the analysis. For internal heat gain, the values specified in the Building Equipment Design Standard [34] were used as reference, and a Likert scale was used to analyze the total points for person density, lighting heat, and equipment heat. The same Likert scale was used for safety factors, and the sum of each coefficient was used in the analysis. The Mann–Whitney U test was used for dichotomous questions, whereas the Kruskal–Wallis test was applied for questions with multiple-choice answers. For variables like internal heat gain and safety factors, where numerical values were directly entered, scores were assigned, and the correlation between the total score and heat source equipment capacity was analyzed. In addition, a power analysis was conducted to assess statistical power based on sample size, effect size, and significance level as a validation of the sample size. The Mann–Whitney U test and Kruskal–Wallis test used in Section 4.2 were conducted using BellCurve for Excel (Social Survey Research Information Co., Ltd, Tokyo, Japan.), and G*Power was used for power analysis. Also, the SEM analysis in Section 4.3 was performed using IBM SPSS AMOS 27 (IBM Japan, Ltd, Tokyo, Japan).

4. Result

4.1. Respondent Attributes

The attributes of respondents are summarized in

Table 4. Respondent information.

Options	n	(%)	Options	n	(%)
Industry			Company Size
General Contractor	32	30	Less than 10	12	11
Architectural Firm	24	23	10–50	19	18
Mechanical and Electrical Contractor	31	29	50–100	22	21
Mechanical and Electrical Design Firm	19	18	More than 100	53	50
Building Use			Building Scale
Private	96	91	Less than 10,000 m2	25	24
Public	10	9	More than 10,000 m2	81	76
Software			Handling of Internal Heat Gain
Only Building Equipment Design Standards	51	48	Should be considered	29	28
Combined Use of Building Equipment Design Standards	39	37	Should not be considered	73	72
Non-use of Building Equipment Design Standards	16	15
Diversity Factor
Considered in design	44	42	-	-	-
Not considered	62	58	-	-	-

and illustrated in Figure 2. The horizontal axis in Figure 2 represents the total score calculated, as shown in Table 3. Responses were obtained from a broad range of industries. However, 50% of the respondents worked for companies with more than 100 mechanical equipment designers. In terms of building use, over 90% of the projects were private and tenant-based, and more than 70% had a floor area exceeding 10,000 m², reflecting the focus on central heat source systems.

Regarding the software used or referenced, more than 80% of the respondents utilized the Building Equipment Design Standards alone or combined with other tools. For heating load calculations, over 70% of respondents felt there was no need to account for internal heat gains, reflecting the strong influence of the Building Equipment Design Standards, which typically do not consider internal heat gains in heating load calculations. However, over 40% did incorporate the diversity factor in their designs.

Figure 2 also shows responses from a range of experience levels. Many designers adhered to the standards for internal heat gain, applying a person density of 0.1–0.2 persons/m², lighting heat of 9–11 W/m², and equipment heat of 15–30 W/m². Similarly, the recommended 30 CMH/person ventilation rate was widely used. While most designers used the safety factor values specified in Table 1, some applied higher values than those set in the standards.

4.2. Statistical Analysis Results for Heat Source Equipment Capacity

To create the model, statistical analyses were conducted to confirm which factors significantly influenced the capacity of heat source equipment. The analysis aimed to determine whether the differences in the distribution of heat source equipment capacity, classified by factors (sub-category in Table 2), are due to random variations or if there are statistically significant differences (at the 5% significance level). The analysis results for the heat source equipment capacity per air-conditioning area are presented in

Table 5. Statistical analysis results for heat source equipment capacity per air-conditioning area.

Options	Cooling					Heating
	n	Median (W/m2)	Mean ±SD (W/m2)	Mean Rank	p-Value	n	Median (W/m2)	Mean ±SD (W/m2)	Mean Rank	p-Value
Industry
General Contractor	32	150	143 ± 34	57.5	p < 0.001	32	100	103 ± 39	49.4	p < 0.001
Architectural Firm	24	100	114 ± 31	30.5		22	70	84 ± 32	33.6
Mechanical and Electrical Contractor	31	148	149 ± 37	59.5		31	100	110 ± 37	54.2
Mechanical and Electrical Design Firm	19	155	156 ± 38	66.1		19	150	146 ± 41	76.9
Company Size
Less than 10	12	160	166 ± 35	73.5	0.107	12	150	160 ± 34	85.9	p < 0.001
10–50	19	125	134 ± 36	48.5		17	100	115 ± 46	55.3
50–100	22	130	136 ± 36	49.4		22	85	94 ± 33	42.1
More than 100	53	140	139 ± 38	52.4		53	100	102 ± 37	48.3
Building Use
Private	96	145	142 ± 37	55.0	0.123	94	100	109 ± 44	52.9	0.658
Public	10	120	125 ± 41	39.3		10	100	104 ± 48	48.5
Building Scale
Less than 10,000 m2	25	150	148 ± 41	59.5	0.463	25	120	123 ± 47	61.9	0.071
More than 10,000 m2	81	140	138 ± 37	51.7		79	100	104 ± 39	49.5
Software
Only Building Equipment Design Standards	51	148	147 ± 38	58.0	0.194	50	100	117 ± 41	58.9	0.103
Combined Use of Building Equipment Design Standards	39	123	132 ± 38	46.5		38	100	103 ± 45	47.3
Non-use of Building Equipment Design Standards	16	150	142 ± 32	56.3		16	100	96 ± 34	50.3
Handling of Internal Heat Gain
Should be considered	-	-	-	-	-	29	80	93 ± 38	39.8	0.006 **
Should not be considered	-	-	-	-		73	100	116 ± 42	57.6
Diversity Factor
Considered in design	44	120	127 ± 35	43.6	0.0051 **	43	80	92 ± 40	39.2	p < 0.001
Not considered	62	150	150 ± 37	60.5		61	120	121 ± 40	61.9

* p < 0.05; ** p < 0.01.

and Figure 3.

For cooling, significant differences were observed concerning industry (p < 0.001) and the diversity factor (p < 0.01). When considering the diversity factor, the median capacity was 120 W/m², while it was 150 W/m² without consideration. This indicates that the capacity of heat source equipment decreases by 20% when the diversity factor is considered.

For heating, significant differences were found concerning industry (p < 0.01), company size (p < 0.01), the handling of internal heat gain (p < 0.01), and the diversity factor (p < 0.001). When internal heat gain was accounted for during heating load calculations as heat gain, the median capacity was 80 W/m², compared to 100 W/m² when not accounted for. This indicates a 20% decrease in heat source equipment capacity when internal heat gain is considered. Furthermore, regarding the diversity factor, the median capacity was 80 W/m² when considered and 120 W/m² when not considered, indicating a 33% reduction in capacity when the diversity factor is considered.

On the other hand, no significant differences were observed for building use, building scale, or software in both cooling and heating. Additionally, no significant correlations were found between heat source equipment capacity, years of experience, internal heat gain, ventilation rate per person, or safety factors.

These results suggest that design methods for handling internal heat gain during heating load calculations and the diversity factor impact the heat source equipment capacity.

The results of the power analysis conducted to assess the adequacy of the sample size are presented in

Table 6. Results of power analysis.

	Power Analysis
	Cooling	Heating
Industry	0.55	0.80
Company Size	0.67	0.77
Building Use	0.40	0.67
Building Sacle	0.68	0.52
Software	0.63	0.50
Handling of Internal Heat Gain	-	0.40
Diversity Factor	0.62	0.57

. Statistical power refers to the probability of correctly detecting an effect when one truly exists in hypothesis testing. A power value of 0.8 or higher is generally considered desirable, while values below 0.50 suggest the need for an increased sample size. In this study, the power values for building use in cooling and handling of internal heat gain were below 0.50, indicating a potential risk that significant differences were not properly detected.

4.3. Integration of Various Factors by SEM

4.3.1. Multiple Indicator Modeling

The preceding sections discussed various factors influencing the design of heat source equipment capacity. Therefore, this section aims to integrate these various factors into a single systematic model. The paths of the model and between models were determined based on prior research [23,24,25,26,27] and the analyses in Section 4.2. The research hypothesis model is shown in Figure 4. The model consists of four elements: personal attributes, such as years of experience, industry, and company size; design conditions, such as building scale, building use, and software; calculation conditions, such as internal heat gain, ventilation rate per person, and safety factors; and design methods, such as handling of internal heat gain in heat load calculation and the diversity factor. It is assumed that calculation conditions and design methods differ based on personal attributes and design conditions and that calculation conditions and design methods influence the heat source equipment capacity. The model was created using the variable reduction method of the Wald test and was ultimately determined based on its goodness of fit.

4.3.2. Path Analysis

The cooling and heating path diagrams are shown in Figure 5. The arrows between the observed variables indicate the direction of causal relationships, and the path coefficients (ranging from −1.00 to 1.00) indicate the strength of these relationships. The gray circles represent error variables (e), which explain variables outside the model that influence the connected variables. The numbers in the upper right corner of the figure indicate the model’s fit indices. The model developed in this study was evaluated using indices such as the Goodness of Fit Index (GFI), Adjusted GFI (AGFI), Comparative Fit Index (CFI), and Root Mean Square Error of Approximation (RMSEA). A GFI, AGFI, and CFI of 0.9 or higher generally indicate a persuasive path diagram and an RMSEA of 0.05 or lower is considered a good fit. The model in the study has GFI = 0.927, AGFI = 0.885, CFI = 0.983, and RMSEA = 0.023 for cooling and GFI = 0.924, AGFI = 0.855, CFI = 0.904, and RMSEA = 0.072 for heating; although the study model’s AGFI is below 0.90, the goodness of fit of the GFI, CFI, and RMSEA is high. Furthermore, this model’s results were considered reasonable compared to previous studies [28,29,30,31,42], so overall, this model was judged to be a good fit. Examining the overall trends of the model, the results were consistent with the research hypothesis model, indicating that personal attributes impact design conditions, which in turn influence calculation conditions and design methods.

In path analysis, the impact of an observed variable is divided into a direct effect, in which the variable directly impacts another variable, and an indirect effect, in which the variable impacts another variable via another variable. When evaluating the strength of the interaction between variables, combining the direct and indirect effects is expected to evaluate the total effect. Based on previous studies by Izawa et al. [43] and Abe et al. [44], the effects were classified as follows:

A relatively large impact	(|Total Effect| ≥ 0.200)
A little impact	(0.100 ≤ |Total Effect| < 0.200)
A slight impact	(0.050 ≤ |Total Effect| < 0.100)
Not particularly effective	(|Total Effect| < 0.050).

The impact of each factor on the others is discussed in the next chapter.

5. Discussion

5.1. Total Effect of Each Design Factor on Heast Source Equipment Capacity

The total effects of each design factor (personal attributes, design conditions, calculation conditions, and design methods) on heat source equipment capacity are presented in

Table 7. Total effect of each design factor on heat source equipment capacity (cooling and heating).

(Cooling)	Personal Attributes				Design Conditions
	Years of Experience		Industry	Company Size	Building Scale	Building Use	Software
Heat Source Equipment Capacity	―		―	―	△	△	―
Total Effect	―		0.03	−0.03	−0.098	−0.05	0.047
	Calculation Conditions				Design Methods
	Internal Heat Gain		Ventilation Rate Per Person	Safety Factors	Handling of Internal Heat Gain		Diversity Factor
Heat Source Equipment Capacity	○		―	◎			◎
Total Effect	0.19		―	0.30			0.29
(Heating)	Personal Attributes				Design Conditions
	Years of Experience		Industry	Company Size	Building Scale	Building Use	Software
Heat Source Equipment Capacity	―		○	―	△	―	―
Total Effect	―		0.13	−0.01	−0.07	−0.03	―
	Calculation Conditions				Design Methods
	Internal Heat Gain		Ventilation Rate Per Person	Safety Factors	Handling of Internal Heat Gain		Diversity Factor
Heat Source Equipment Capacity			―	○	○		◎
Total Effect			―	0.12	0.11		0.33

◎: 0.200 ≤ | Total Effect | (Makes a relatively large impact). ○: 0.100 ≤ | Total Effect | < 0.200 (Make a little impact). △: 0.050 ≤ | Total Effect | < 0.100 (Make a slight impact). ―: 0.050 ≤ | Total Effect | < 0.050 (Not a particularly effective).

. The results confirm that the internal heat gain, safety factors, handling of internal heat gain, and diversity factor have relatively large impact on heat source equipment capacity. The following key findings can be derived from Table 7:

• A lower internal heat gain setting leads to a smaller heat source equipment capacity.
• A smaller safety factor setting results in a smaller heat source equipment capacity.
• Considering internal heat gain in heating load calculations reduces heat source equipment capacity.
• Incorporating the diversity factor into the design leads to a smaller heat source equipment capacity.

These findings align with previous studies [25,26,27] and indicate that the adoption of appropriate design methods and designs based on actual building usage conditions are effective in optimizing heat source equipment capacity. Furthermore, the results emphasize the importance of a comprehensive design approach to achieving proper capacity optimization. In particular, the total effect of the diversity factor was 0.29 for cooling and 0.33 for heating, which was larger compared to other factors. This suggests that considering the diversity factor in actual design practice is especially effective in optimizing the heat source equipment capacity.

5.2. Total Effect of Personal Attribute, Design Conditions and Calculation Conditions on Design Methods

The total effects of personal attributes, design conditions, and calculation conditions on design methods are presented in

Table 8. Total effect of personal attributes, design conditions, and calculation conditions on design methods (cooling and heating).

(Cooling)	Personal Attributes				Design Conditions
	Years of Experience		Industry	Company Size	Building Scale	Building Use	Software
Handling of Internal Heat Gain
Total Effect
Diversity Factor	―		―	○	◎	―	―
Total Effect	―		0.08	−0.11	−0.34	―	―
	Calculation Conditions				Design Methods
	Internal Heat Gain		Ventilation Rate Per Person	Safety Factors	Handling of Internal Heat Gain		Diversity Factor
Handling of Internal Heat Gain
Total Effect
Diversity Factor	―		―	―
Total Effect	―		―	―
(Heating)	Personal Attributes				Design Conditions
	Years of Experience		Industry	Company Size	Building Scale	Building Use	Software
Handling of Internal Heat Gain	―		◎	○	△	―	―
Total Effect	―		0.40	0.12	−0.07	−0.048	―
Diversity Factor	―		◎	△	○	○	―
Total Effect	―		0.27	−0.07	−0.19	−0.13	―
	Calculation Conditions				Design Methods
	Internal Heat Gain		Ventilation Rate Per Person	Safety Factors	Handling of Internal Heat Gain		Diversity Factor
Handling of Internal Heat Gain			―	―
Total Effect			―	―
Diversity Factor			―	―
Total Effect			―	―

◎: 0.200 ≤ | Total Effect | (Makes a relatively large impact). ○: 0.100 ≤ | Total Effect | < 0.200 (Make a little impact). △: 0.050 ≤ | Total Effect | < 0.100 (Make a slight impact). ―: 0.050 ≤ | Total Effect | < 0.050 (Not a particularly effective).

. The results confirm that industry has a relatively large impact on the handling of internal heat gain, while building scale has a relatively large impact on the diversity factor. The following key findings can be derived from Table 8:

• General Contractors and Architectural Firms tend to consider internal heat gain in heating load calculations more than Mechanical and Electrical Contractors and Mechanical and Electrical Design Firms.
• The larger the building scale, the more likely the diversity factor is incorporated into the design.

Regarding the diversity factor, larger buildings generally have fewer instances where multiple functions are used simultaneously, making it easier to incorporate the diversity factor into the design. As indicated in Section 5.1, the diversity factor is considered the most effective factor in optimizing heat source equipment capacity. Although its application may be challenging for buildings smaller than 10,000 m², it should be actively considered for buildings of 10,000 m² or larger. Notably, this survey also inquired about specific values of the diversity factor, with an average of approximately 80%.

On the other hand, industry correlates with company size, and smaller companies tend to neglect the consideration of internal heat gain in heating load calculations. This can be attributed to the fact that larger companies have well-established internal standards for estimating internal heat gain, whereas smaller companies, lacking explicit guidelines in Building Equipment Design Standards, face uncertainty in determining appropriate values. However, as demonstrated in Section 5.1, considering internal heat gain in heating load calculations is effective in optimizing heat source equipment capacity, highlighting the need for explicit guidelines within Building Equipment Design Standards. Similarly to the diversity factor, the survey also inquired about specific values of the handling of internal heat gain. On average, lighting heat accounted for approximately 60%, while person density and equipment heat each accounted for around 30%.

Ultimately, the settings for internal heat gain and safety factors, as well as the selection of design methods, largely depend on the judgment of individual designers. The results of this study indicate that such design decisions significantly influence heat source equipment capacity. Previous research [45,46] has also demonstrated that designers’ decisions directly impact the final energy efficiency of buildings. Therefore, instead of passively relying on standard design practices, it is crucial for designers to consciously adopt appropriate design approaches tailored to each project.

5.3. Total Effect of Personal Attribute, Design Conditions, and Design Methods on Calculation Conditions

The total effects of personal attributes, design conditions, and design methods on calculation conditions are presented in

Table 9. Total effect of personal attributes, design conditions, and design methods on calculation conditions (cooling and heating).

(Cooling)	Personal Attributes				Design Conditions
	Years of Experience		Industry	Company Size	Building Scale	Building Use	Software
Internal Heat Gain	―		―	―	△	◎	◎
Total Effect	―		0.02	0.03	0.09	−0.27	−0.24
Ventilation Rates Per Person	―		―	―	―	―	―
Total Effect	―		―	―	―	―	―
Safety Factors	―		―	―	△	―	―
Total Effect	―		0.02	−0.02	−0.07	―	―
	Calculation Conditions				Design Methods
	Internal Heat Gain		Ventilation Rate Per Person	Safety Factors	Handling of Internal Heat Gain		Diversity Factor
Internal Heat Gain							◎
Total Effect							−0.28
Ventilation Rates Per Person							―
Total Effect							―
Safety Factors							◎
Total Effect							0.20
(Heating)	Personal Attributes				Design Conditions
	Years of Experience		Industry	Company Size	Building Scale	Building Use	Software
Internal Heat Gain
Total Effect
Ventilation Rates Per Person
Total Effect
Safety Factors	―		△	―	―	○	―
Total Effect	―		0.09	−0.02	−0.04	0.12	―
	Calculation Conditions				Design Methods
	Internal Heat Gain		Ventilation Rate Per Person	Safety Factors	Handling of Internal Heat Gain		Diversity Factor
Internal Heat Gain
Total Effect
Ventilation Rates Per Person
Total Effect
Safety Factors					―		◎
Total Effect					―		0.20

◎: 0.200 ≤ | Total Effect | (Makes a relatively large impact). ○: 0.100 ≤ | Total Effect | < 0.200 (Make a little impact). △: 0.050 ≤ | Total Effect | < 0.100 (Make a slight impact). ―: 0.050 ≤ | Total Effect | < 0.050 (Not a particularly).

. The results confirm that building use has a relatively large impact on internal heat gain, while software affects internal heat gain, the diversity factor influences internal heat gain, and the diversity factor also has a large impact on safety factors. The following key findings can be derived from Table 9:

• Public buildings tend to have lower internal heat gain settings compared to private buildings.
• Designers using software that does not comply with Building Equipment Design Standards tend to set lower internal heat gain values.
• Designers who consider the diversity factor tend to set higher internal heat gain values.
• Designers who consider the diversity factor tend to set lower safety factors.

Public buildings are subject to strict adherence to Building Equipment Design Standards, whereas in private buildings, particularly in tenant-occupied spaces, the intended use of the building is often unclear, leading to higher internal heat gain settings. Additionally, software that does not comply with Building Equipment Design Standards allows for a more detailed evaluation of buildings, such as considering daily schedules, enabling more precise internal heat gain settings, which often results in lower values. The results of this study suggest that internal heat gain tends to be higher in private buildings compared to public buildings. Therefore, design strategies should be implemented to reduce internal heat gain, such as considering time-dependent variations in internal heat gain.

On the other hand, designers who consider the diversity factor tend to reduce safety factors to avoid overdesign. However, as a precaution against insufficient capacity, they also avoid setting internal heat gain values too low, which explains their tendency to set relatively higher internal heat gain values. Rather than excessively designing all factors to prevent capacity shortages, it is essential to adopt a balanced approach, for instance, by considering the diversity factor to avoid overdesign, when internal heat gain is set relatively high.

5.4. Total Effect of Personal Attributes on Design Conditions

The total effects of personal attributes on design conditions are presented in

Table 10. Total effect of personal attributes on design conditions (cooling and heating).

(Cooling)	Personal Attributes				Design Conditions
	Years of Experience		Industry	Company Size	Building Scale	Building Use	Software
Building Scale	―		◎	◎
Total Effect	―		−0.23	0.31
Building Use	―		◎	―
Total Effect	―		0.21	―
Software	―		◎	―
Total Effect	―		−0.40	―
	Calculation Conditions				Design Methods
	Internal Heat Gain		Ventilation Rate Per Person	Safety Factors	Handling of Internal Heat Gain		Diversity Factor
Building Scale
Total Effect
Building Use
Total Effect
Software
Total Effect
(Heating)	Personal Attributes				Design Conditions
	Years of Experience		Industry	Company Size	Building Scale	Building Use	Software
Building Scale	―		○	◎
Total Effect	―		−0.18	0.38
Building Use	―		◎	―
Total Effect	―		0.24	―
Software	―		◎	―
Total Effect	―		0.09	−0.02
	Calculation Conditions				Design Methods
	Internal Heat Gain		Ventilation Rate Per Person	Safety Factors	Handling of Internal Heat Gain		Diversity Factor
Building Scale
Total Effect
Building Use
Total Effect
Software
Total Effect

◎: 0.200 ≤ | Total Effect | (Makes a relatively large impact). ○: 0.100 ≤ | Total Effect | < 0.200 (Make a little impact). △: 0.050 ≤ | Total Effect | < 0.100 (Make a slight impact). ―: 0.050 ≤ | Total Effect | < 0.050 (Not a particularly).

. The results confirm that industry has a relatively large impact on building scale, building use, and software, while company size largely influences building scale. The following key findings can be derived from Table 10:

• General Contractors and Architectural Firms handle larger-scale buildings, more private-sector projects, and tend to use software that does not comply with Building Equipment Design Standards, compared to Mechanical and Electrical Contractors and Mechanical and Electrical Design Firms.
• The larger the company size, the larger the building scale.

Smaller firms use software that is relatively compliant with Building Equipment Design Standards, so there is a need for software development and training programs that can be easily used by smaller firms.

6. Limitation

In this study, we developed a model to evaluate the impact of various factors on heat source equipment capacity. However, the following limitations should be noted.

First, this questionnaire targeted designing newly constructed office buildings. Therefore, the model reflects relationships specific to office building design in Japan. Additionally, the questionnaire results indicate that the proportion of public buildings was relatively low at 9%, and 50% of respondents were from companies with over 100 mechanical equipment designers, which suggests a potential bias and lack of diversity in the sample size in the responses. Furthermore, this study limited the model to Region 6, the energy-conservation regional classification that includes Tokyo, Osaka, and Aichi, a cooling-dominated warm region for office buildings. It is important to note that the model may vary for heating-dominated cold regions like Hokkaido or hot and humid regions like Okinawa, and further investigation is required to adapt the model to these areas.

Second, regarding calculation conditions, this study followed the values set by Japan’s Building Equipment Design Standards [34], which differ from those in ASHRAE standards [47]. Additionally, while the model incorporated “considering” or “not considering” design methods, specific numerical values were not included.

Third, this study focused solely on maximum heat load calculation in mechanical equipment design. However, factors beyond those considered in this study—such as the building’s operational schedule and occupant energy-saving behaviors [48]—will obviously have a significant impact on the final heat source equipment capacity. Future research should explore which factors influence heat source equipment capacity and further refine the model.

7. Conclusions

This study focused on the design of central heat source systems in office buildings located in warm regions of Japan, analyzing the stepwise interrelationships between various design factors and heat source equipment capacity. Rather than treating each design factor as an independent and isolated factor, this study conducted a structural and comprehensive analysis of the relationships between design factors and equipment capacity while also considering the interdependencies among design factors. This novel perspective, which has not been explored in previous research, represents the most significant contribution of this study. The key findings are summarized as follows.

(1)

It was clarified that considering the diversity factor is the most effective approach for optimizing heat source equipment capacity. By incorporating the diversity factor, the median capacity of cooling equipment can be reduced by 20%, while heating equipment capacity can be reduced by 33%. Additionally, the consideration of the diversity factor is significantly influenced by building scale, which varies depending on industry and company size.

(2)

It was demonstrated that accounting for internal heat gain in heating load calculations can reduce heating equipment capacity by 20%. Furthermore, industry and company size influence the handling of internal heat gain, leading to different approaches depending on these factors.

(3)

Internal heat gain and safety factors impact heat source equipment capacity, indicating that appropriate design based on actual building usage conditions is effective in optimizing heat source equipment capacity. Moreover, the intended building use (private or public) and software used for design influence internal heat gain, and these factors, in turn, vary depending on industry and company size.

The influence structure of design factors and heat source equipment capacity, organized based on the above findings, is shown in Figure 6 as the conclusion of this study.

Finally, although the diversity factor, which was suggested as effective in optimizing heat source equipment capacity in this study, is not currently specified in the Building Equipment Design Standards, it is necessary for the government to establish standardized values to ensure that they can be universally applied. Additionally, understanding the current state of internal heat gain, which is likely to have been significantly affected by COVID-19, is an important issue. Further research should incorporate factors beyond those addressed in this study and expand the analysis across various regions, which is expected to provide an effective approach to optimizing heat source equipment capacity.